Avoiding zero probability events when computing Value at Risk contributions
Yuri F. Saporito, Rodrigo S. Targino, Takaaki Koike
This paper is concerned with the process of risk allocation for a generic
multivariate model when the risk measure is chosen as the Value-at-Risk (VaR).
We recast the traditional Euler contributions from an expectation conditional
on an event of zero probability to a ratio involving conditional expectations
whose conditioning events have strictly positive probability. We derive an
analytical form of the proposed representation of VaR contributions for various
parametric models. Our numerical experiments show that the estimator using this
novel representation outperforms the standard Monte Carlo estimator in terms of
bias and variance. Moreover, unlike the existing estimators, the proposed
estimator is free from hyperparameters under a parametric setting.